Sample-based observability of linear discrete-time systems

TL;DR

This paper investigates how to reconstruct the state of linear discrete-time systems when measurements are sampled irregularly, identifying system behaviors that cause sampling issues and proposing schemes to ensure observability.

Contribution

It introduces a novel analysis of sample-based observability in linear systems and develops sampling schemes tailored to different system behaviors.

Findings

Certain systems exhibit pathological sampling behaviors.

Proposed sampling schemes enable state reconstruction.

Analysis guides optimal sampling strategies.

Abstract

In this work, sample-based observability of linear discrete-time systems is studied. That is, we consider the case where the system output measurements are not available at every time instance. It is shown that some discrete-time systems exhibit particular behaviors that lead to pathological sampling. Depending on the characteristics of the system, different sampling schemes are developed that allow the system state to be reconstructed.